Six years later he applied for the chair of natural philosophy in his own university, but again without success, and in 1773 he was offered and accepted the benefice of the united parishes of Liff and Benvie, vacant by the death of his father. Playfair continued, however, his mathematical and physical studies, and in 1782 he resigned his charge to become the tutor of Ferguson of Raith. By this arrangement, Playfair was able to be frequently in Edinburgh and to cultivate the literary and scientific society for which it was at that time specially distinguished. In particular, he attended the natural history course of John Walker. Through Nevil Maskelyne, whose acquaintance he had first made in the course of the celebrated Schiehallion experiments in 1774, he also gained access to the scientific circles of London. In 1785 when Dugald Stewart succeeded Ferguson in the Edinburgh chair of moral philosophy, Playfair succeeded the former in that of mathematics.

In 1795 Playfair published an alternative, more stringent formulation of Euclid's parallel postulate, which is now called Playfair's axiom; though the axiom bears Playfair's name, he did not create it, but credited others, in particular William Ludlam, with the prior use of it.[2]

In 1802, Playfair published his celebrated volume entitled Illustrations of the Huttonian Theory of the Earth. The influence exerted by James Hutton on the development of geology is thought to be largely due to its publication. In 1805 Playfair exchanged the chair of mathematics for that of natural philosophy in succession to John Robison, whom also he succeeded as general secretary to the Royal Society of Edinburgh. He took a prominent part, on the liberal side, in the ecclesiastical controversy that arose in connection with Sir John Leslie's appointment to the post he had vacated, and published a satirical letter (1806).

John's brothers were architect James Playfair, solicitor Robert Playfair and engineer William Playfair. His nephew, William Henry Playfair (1790–1857) was an eminent architect in Scotland. Although an eminent man, Playfair was buried in an unmarked grave in Old Calton Burial Ground, on Waterloo Place in Edinburgh. His, and his brother, James's graves were marked by a plaque unveiled in 2011 following a local campaign.[4] The monument to his memory by William Henry Playfair, on Calton Hill,[5] is visible from the spot. In later life he admired and proposed to the wealthy widow Jane Apreece. She turned him down and married the younger and more famous Sir Humphry Davy.[6]

A four-volume collected edition of Playfair's works, with a memoir by James G. Playfair, appeared at Edinburgh in 1822.[9]

His writings include a number of essays contributed to the Edinburgh Review from 1804 onwards, various papers in the Philosophical Transactions of the Royal Society (including his earliest publication, "On the Arithmetic of Impossible Quantities", 1779, and an "Account of the Lithological Survey of Schehallion", 1811) and in the Transactions of the Royal Society of Edinburgh ("On the Causes which Affect the Accuracy of Barometrical Measurements" and others), the articles "Aepinus" and "Physical Astronomy", and a "Dissertation on the Progress of Mathematical and Physical Science since the Revival of Learning in Europe" in the Encyclopædia Britannica (Supplement to fourth, fifth and sixth editions).

His Elements of Geometry first appeared in 1795 and has passed through many editions; his Outlines of Natural Philosophy (2 vols., 1812–1816) consist of the propositions and formulae which were the basis of his class lectures. Playfair's contributions to pure mathematics were not considerable, his papers "On the Arithmetic of Impossible Quantities" and "On the Causes which Affect the Accuracy of Barometrical Measurements", and his Elements of Geometry, all already referred to, being the most important. His lives of Matthew Stewart, Hutton, and Robison, many of his reviews, and above all his "Dissertation" are of the utmost value.

^J. Playfair and Euclid, Elements of geometry; containing the first six books of Euclid, with two books on the geometry of solids. To which are added, elements of plane and spherical trigonometry, J.B. Lippincott & Co, 1860, p. 291. Available online from Google Books. See also Cajori's A History of Mathematics.